Let me give you a definitive answer. It depends. Dont believe me? Ask any former fighter pilot or someone who knows what he's talking about to answer this. I bet they will say the same. Given the infinite amount of factors eg. Aircraft loadout, fuel, weight, altitude, airspeed, missile pK, countermeasure effectiveness and the general concept of who shoots first will win etc, it is literally not possible to answer your question. Anyone who says otherwise is not considering these or does not know what they are talking about. I can however, give you a likely winner.
PS: I won't talk much about gun kills, as it's a simple concept and you're normally going down if someone guns you. Did I also mention the probability of a missile hitting a target when it is dispensing countermeasures is literally like rolling a dice? You never know the outcome.
Now prepare yourself for a very long article on the capabilities and vulnerabilities of each aircraft. For simplicity's sake, I will use the best combat loadout that is normally taken for each individual aircraft.
F-14 Tomcat
Now, it is worth mentioning that the F-14 was designed for fleet air defense and is more of an interceptor than anything else. It can dogfight, just it isn't very good at it.
The F-14 normally comes equipped with 4x AIM-7 Sparrows (semi-active radar guided), 2x AIM-54 Phoenix (active radar guided) and 2x AIM-9 Sidewinder (heatseeking) missiles and a 20mm M61A1 Vulcan. As you can probably tell from it's combat loadout, it has a fair bit of long range firepower, not so much on the dogfighting side of things. That being said, the F-14 could dogfight sufficiently well given it had enough energy. However, the wing sweep on the F-14 was commonly complained about, as it was a dead giveaway on how much energy the aircraft had retained. In a dogfight, if you lose energy, you lose the fight (some Russian aircraft excluded). Now, at close ranges (especially furballs), most fighter pilots would use heatseekers as they are more maneuverable and are generally better suited for close ranges. Now, as previously mentioned, I can't give an answer. No one can. But I will state the one that is most likely to survive. Moving on.
F-15C Eagle
The F-15 is a remarkable fighter, with absolutely no losses in aerial engagements. Now, that might lead you to believe the F-15 is invincible. I can tell you it isn't. I know how it flies, how it handles under different situations and how the weapon systems and countermeasures work. The main advantage of the F-15 is in fact, it's maneuverability and missiles.
The F-15C comes equipped with a load of either 4x AIM-120 AMRAAM (active radar guided) and 4x AIM-9 Sidewinder (heatseeking) missiles OR 6x AIM-120 and 2x AIM-9. The F-15 has the same Vulcan that is used on the F-14. For the best case scenario, I will use the first loadout. With 4 heatseekers, the F-15 definitely stands a better chance of maneuvering for a kill against a target, and has more ordinance to hand feed to said target. The aircraft, despite it's delta wing design, turns pretty hard at speeds at or above 300 knots, and could pull some pretty high alpha at speeds lower than 300 knots for snapshots at targets. However, all US aircraft are conditioned for long range BVR combat. Thus they share common similarities with each other. While the AMRAAM is definitely better against maneuvering targets compared to the Phoenix, it still isn't the best at close ranges.
F-16C Fighting Falcon (Viper)
This is something I have to stress right from the beginning. The F-16 is a VERY GOOD dogfighter. The main advantage of the F-16 is its maneuverability, which it excels in. Having a relaxed static stability/fly-by-wire system, the F-16 was designed to be unstable from the get-go, and that's where it gets it's maneuverability from.
The F-16 can carry a load of 6x AIM-9s to go with its Vulcan cannon. This makes it shine as a dogfighter and it can pull hard turns and maneuvers that some aircraft just can't do because of their respective aerodynamic qualities.
F/A-18C Hornet
It should be noted that the F/A-18 was not designed solely for air combat. Then again, so did the F-16, so the F/A-18 should be pretty good right? Well, it depends. The Hornet can pull some pretty insane Alpha and turns fairly tightly for an aircraft of its size and weight. In a dogfight, it stands just as good a chance as any other aircraft. With a HMCS, the F/A-18 has the ability to lock on to any aircraft within the aircraft's visual cueing cone.
The Hornet can carry a maximum load of 4x AIM-9s and 2x AIM-7s OR AIM-120s. I'm actually running out of ideas on what to say here, until we get to the Russians at least. You know the drill. AIM-9 is good. AIM-120 can even used but it not the most ideal when really close to an enemy aircraft.
Mirage-2000C
Ah the good ol' Mirage-2000. It's a fun aircraft to fly. Not so much in the way of dogfighting though. I wrote an answer for this aircraft a few days ago regarding air combat. Now, the Mirage is a delta wing design, which means less lift. But, unlike the F-15, it doesn't have traditional control surfaces. The Mirage uses elevons that function for both roll and pitch, which is the same as the F-15. The only problem, being they are mounted on the wings themselves, which equates to less pitch control at low speeds, thus not making it the best dogfighter out there.
The M-2000 is equipped with 2x Matra Super 530s (semi-active radar guided) and 2x Matra R-550 Magic IIs (heatseeking). It can hold it's own in a dogfight, but I doubt it does too well in a furball. If you really want to know, at low speeds, the delta wing on the Mirage limits it's pitch authority so bad that the 3rd gen F-5E can turn with it.
Eurofighter Typhoon (we're halfway down the list, YAY!)
The Eurofighter Typhoon. Very beautiful aircraft indeed. Unlike traditional delta wing designs like the M-2000C, the Typhoon is exceptionally maneuverable at both low and high speeds, thanks to it's fly-by-wire system and use of canards. The Eurofighter is one of the best on this list, and may very well win in a furball. The reason behind this is it has a HMCS and lock-on-after-launch (LOAL) capability. However, let's not jump to conclusions.
The Eurofighter carries… err… well I'll be completely honest. I don't really know the amount of air to air weaponry it can carry. However, the typical Eurofighter carries 6x AIM-120 and 2x AIM-132 ASRAAM or IRIS-T (heatseeking) missiles. Since we can't really talk about how good the missiles are because it's impossible to predict real life situations, I won't bother.
JAS-39 Gripen
I don't really know what to say for the Gripen. It is essentially a Eurofighter by aerodynamic design, with a similar fly-by-wire system and canards for improved stability and maneuverability and a HMCS as well. Therefore, I will move straight to the weapon systems. Besides, I don't really know the Gripen that well, so I won't pretend to.
In the best case scenario, a Gripen may carry 6x AIM-9s OR IRIS-T OR A-Darter (heatseeking) missiles.
Dassault Rafale
WHY DO THEY DO THIS? It's pretty much exactly the same as both the Eurofighter and the Gripen in terms of agility, avionics and weapons. Can we skip this one?
The Rafale can carry a number of Magic IIs and MICA (radar guided/infrared homing) missiles.
Mikoyan Gurevich MiG-29S
Now we're getting to the fun stuff. Like the American aircraft, I actually don't need to refer to any external sources for this. Now, the MiG-29's armament is different depending on the model, so I'll use the MiG-29S. The Fulcrum can perform hard sustained turns for long periods and is excellent in the dogfighting department with it's powerful engines and most importantly, the High Off Boresight (HOBS) missile capability and Infrared Search and Track (IRST) sensor which gives the Russian aircraft a major edge in close ranges. By simply pointing his head and looking at an enemy aircraft, the pilot can lock the target and launch a missile within a +-60° cone in front of the aircraft. It doesn't help the offending pilot that the Russian R-73 heatseekers are supermaneuverable and can literally turn almost 180° for target interception.
The MiG-29S is capable of carrying 2x R-77 (active radar guided), 2x R-27ER/ET/R/T/P (radar guided/heatseeking depending on model) and 2x R-73 (highly maneuverable heatseeking) missiles. The highlight here is the R-73 which is, for lack of a better word, stupidly maneuverable, though limited in range compared to its counterparts from other countries.
Sukhoi Su-27
One of my personal favourites. I know her like the back of my hand. The Su-27 is supermaneuverable, can turn incredibly tight, is able to perform Pugachev's Cobra to either snap it's nose close to an enemy for it's pilot to use the HMD and HOBS missiles or to break the radar lock of an enemy aircraft. It has a very long range and carried a huge complement of missiles.
The Flanker carries multiple loadouts: 6x R-27ER/ET/EP/R/T/P, 2x R-73 and 2x wingtip mounted SPS-171 “Sorbtsiya” ECM pods OR 4x R-27ER/ET/EP/R/T/P, 4x R-73 and 2x wingtip mounted SPS-171 “Sorbtsiya” ECM pods OR 4x R-27ER/ET/EP/R/T/P and 6x R-73.
I know where to find a manual for it if you want one.
Mikoyan Gurevich MiG-25
Ugh. I'm not even posting a photo. The MiG-25 is a bad dogfighter, like very bad. It's only advantage was it's speed, and that was only at high altitude. It is slower compared to other aircraft at sea level. Plus, with a maximum G-loading of 4.5G, it doesn't really do well.
The MiG-25 carries a load of 4x R-40RD/TD (long range semi-active radar guided/heatseeking respectively) OR 2x R-23 OR 2x R-60 OR 4x R-73.
Harrier
Remark: This thing isn't a very good fighter. In fact, it isn't one.
As far as I understand the Harrier, it uhh… just won't survive in a furball. The MiG-25 stands a better chance. No, really.
The Harrier can equip 4x AIM-9s. For the fancy AV-8B Plus, which actually has a radar fitted, it can fire 6x AIM-120s. For self defense mind you.
Conclusion
Now comes the likely winners of the furball. I say winners because I can't say. It only takes a missile to destroy an aircraft, and it doesn't matter where said missile comes from. Whether it comes from an A-10 or F-5.
So the likely winners would be: F-16, F/A-18, Eurofighter, Gripen, Rafale, MiG-29 and Su-27.
Note: The Harrier is a good aircraft, I can tell you that. But by no means is it a dogfighter even with VSTOL nozzle capabilities.
